Being from Montana a relatively dry state I am used to normal treating my saddles, bridles and other leather tack with quality cleaning products like Farnam's Leather new and my tack stayed in excellent condition and was ready to use the next spring.
Last fall I moved to northern california in November leaving my tack carefully stored in my horse trailer's tack/dressing room. To my surprise and horror just a few months later I discovered that everything was covered in thick green mold! The darker leather items seamed to have more mold than the lighter colored items. I am guessing this is because darker leather normally contains more moisture than the lighter tan times.
1) Store your tack in large plastic tack tubs during the winter. Rubbermaid tubs seem to work well.
2) If storing your tack in a tack room in humid climates remember to us dehumidifiers. I found a nice one on ebay that is in a box with an indicator when it is time to change it too keep the area dry and therefore mold free.
3) Many people choose to bring their treasured horse tack in the house for the winter to protect it for the winter.
4) I have found leather conditions with "mold inhibitor" that I have started to use. Haven't seen the results yet. We shall see how this winter goes.